Question

if line $y=√3$ meets the graph$y=tanx$where$x€(0, π/2 )$in k points. what is k equal to?​

Answer 1

❇Answer❇

☣Concept :

• The solution set for the intersection of the two graphs say y = f(x) and y = g(x) will contain the solution of the equation f(x) = g(x)

☣Given :

There are two equation.

• y =√3
• y=tan x

☣Solution :

The intersection of this two graph will be the solution set for the equation .

$\bf \pink {\implies \: \sqrt{3} = tan \: x}$

$\bf \underline{Taking \: {tan}^{ - 1} \: \: on \: both \: side}$

$\bf \pink {\implies \: {tan}^{ - 1} ( \sqrt{3} ) = {tan}^{ - 1} (tan \: x)}$

☣WKT,

$\bf \underline { {tan}^{ - 1} (tan \: x) \: is \: \: equal \: \: to \: x}$

$\bf \pink { \implies \: {tan}^{ - 1}( \sqrt{3}) = x}$

$\bf \underline{the \: \frac{\pi}{3} \: is \: the \: \: principal \: \: value \: \: as}$

$\bf \pink{ \implies \: tan \bigg( \frac{\pi}{3} \bigg) = \sqrt{3}}$

☯The general solution for the above equation will be,

${\sf{ \boxed{ \sf{x = n\pi + \frac{\pi}{3} \: \: and \: \: n \: \: is \: the \: integer}}}}$

☣Given that

$Range \:\: on \:\: the \: x\: is\:$

$\bf \pink{x€\bigg(0, \frac{\pi}{2} \bigg)}$

• The solution set of the intersection of the graph is .. -2π/3 , π/3, 4π/3...

• But only one value of the solution lies in the range.

Since K is the number of solution points for the intersection of the graph y =√3 and y =tan x in the range x €(0, π/2) , so we can say that k=1

☣Note :

Refer the attachment for the graph.

• From the graph there is only one intersection point

Answer 2

Step-by-step explanation:

❇Answer❇

☣Concept :

The solution set for the intersection of the two graphs say y = f(x) and y = g(x) will contain the solution of the equation f(x) = g(x)

☣Given :

There are two equation.

y =√3

y=tan x

☣Solution :

The intersection of this two graph will be the solution set for the equation .